I'm trying to make my plane (ground) explode up into the air
Introduction

The discribed method is only one of several methods to create an animation of a ground explosion and it's the fastest method that I know. 
It will cover only the basics of preparing the plane, creating the debris and setting up the physics to get this result. 




I won't go over the task of texturing here, since BlenderSE is not the best medium to create long tutorials. A good method to texture the debris is described in one of the Timster's videos which you can find here: Project Assets: Low Poly Rubble  

Blend file: 



Prerequisites

In order to get nice debris, we are going to use the Cell Fracture addon. Hit Ctrl+Alt+U to show the User Preferences, to to the Addon Panel and type "cell" into the search field. On the right side, activate "Object: Cell Fracture", (if you plan to use the addon regularly, you also might hit "Save User Settings"). Close User Preferences.



Preparation of the Base Meshes

Add a plane, resize it to a reasonable size and subdivide it (If you already have a plane or a terrain of some sort, you can use that as well, as long as it has not too many faces). Move your vertices around in the area where the explosion should take place, until you have a nice uneven jagged area. To get a nice shape you might enable proportional editing mode for the rough shape and disable it again for the finer details. 




Select the faces for the hole, then press Numpad 1 to go to front view, then press E and Z extrude the vertices down on the z-axis. 




Enable Face Select, turn off "Limit selection to visible" and select all the faces below the ground plane. Hit Shift+D to duplicate them, then hit P and select "Selection" to create a new object out of the duplicated mesh. Tab into Object Mode, hit M and 2 to move the new object to Layer 2. 



You should now have two objects like these below, each on its own layer. 



Rename the object on Layer 1 into "ground" and the object on Layer 2 into "debris". 




Go to Layer 2 and tab into Edit Mode. In front view (Numpad 1), enable "select vertices", "Snap during transform", set "Type of Element to snap to" to vertex and also enable "Automatically merge Vertices". Select all vertices of the ground plane. Hit G and Z to move them up on the z-axis until it snaps and fuses with the original mesh. 




Still in Edit mode, hit A until everything is selected, then hit Ctrl+N to make the normals of your mesh face outwards. Select the vertices of the ground plane again and move them on the z-axis until the height of your mesh is about 3/4 of its original size. Then scale the ground plane down to 0.9 (Hit S then 0.9). 




Hit Ctrl+R to add two loopcuts (Mouse Wheel up), then tab into object mode.  



Add a Subdivision Surface modifier, set its type to "Simple" and the Numbers to 3 and click "Apply". Then go to the Tool Panel (T), go to "Tools" panel and click the Cell Fracture Button (it should have been added by the Cell Fracture addon, see Prerequisites). In the now opened Settings Window, set "Source Limit" to 250, select "Random" and click OK. 




You should then see something similar to to this in the 3D viewport. 




You now still have your original debris mesh in Layer 2 and the newly generated fragments in Layer 3. Switch to Layer 3, then go to the Outliner and select the mesh that should be called "debris_cell". This is now your active mesh. Move your mouse pointer to the 3D view and hit A to select all objects. 




Physics

Go to the Tool Panel, then to "Physics" and click on "Add Active" (note how the outline of your selected objects turn from yellow to green in the 3D Viewport). Then go to the Properties Window, switch to the Physics Panel, go to "Rigid Body Collision", enable "Collision Margin" and change it to 0.15 (this influences the force). Go back to Tool Panel - Physics and click "Copy from Active" to apply the changes to all the selected objects. Reminder: You'll have to do this every time, when you change something in the Physics Panel!




Play Animation

Go to Layer 1, select your ground mesh, then go to the Tool Panel - Physics and click on "Add Passive". The ground mesh now should also have a green outline. Go back to Layer 3, hit A until everything is selected, then M and 1 so move everything to Layer 1. Hit A until nothing is selected go to the timeline area and hit the "Play Animation" button. 




Enjoy!